An airliner maintaining a constant elevation of 2 miles passes over an airport at noon traveling 500 mi/hr due west. At 1:00 PM, another airliner passes over the same airport at the same elevation traveling due north at 550 mi/h. Assuming both airliners maintain the (equal) elevations, how fast is the distance between them changing at 2:30 PM

Step-by-step explanation:

Let suppose that airliners travel at constant speed. The equations for travelled distance of each airplane with respect to origin are respectively:

First airplane

Where t is the time measured in hours.

Since north and west are perpendicular to each other, the staight distance between airliners can modelled by means of the Pythagorean Theorem:

Rate of change of such distance can be found by the deriving the expression in terms of time:

Where and , respectively. Distances of each airliner at 2:30 PM are:

The rate of change is:

probably the last option

step-by-step explanation: